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Matrices — Mathematics STD 10 — Question

ICSE BoardEnglish MediumSTD 10MathematicsMatrices3 Marks
Question
If $M=\left[\begin{array}{ll}1 & 2 \\ 2 & 1\end{array}\right]$ and $I$ is a unit matrix of the same order as that of $M$ Show that $M^2=2 M+3 I$
✓

Answer

$\begin{aligned} & M^2=\left(\begin{array}{ll}1 & 2 \\ 2 & 1\end{array}\right)[(1,2)(2,1)] \end{aligned} $
$ =\left(\begin{array}{ll}1+4 & 2+2 \\ 2+2 & 4+1\end{array}\right)  $
$ =\left(\begin{array}{ll}5 & 4 \\ 4 & 5\end{array}\right)  $
$ 2 M+3 I=2\left(\begin{array}{ll}1 & 2 \\ 2 & 1\end{array}\right)+3\left(\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right)  $
$ =\left(\begin{array}{ll}2 & 4 \\ 4 & 2\end{array}\right)+\left(\begin{array}{ll}3 & 0 \\ 0 & 3\end{array}\right)  $
$ =\left(\begin{array}{ll}5 & 4 \\ 4 & 5\end{array}\right)$

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